High school geometry

Question 1

What is a Reflexive property?
What are some relations that use it?
What are some relations that don’t?

Answer 1

When a relation has a reflexive property, it means that the relation is always true between a thing and itself. So A (relation) A.
Use it:
Equality( 3=3)
congruence
similarity
Don’t use it:
strict inequality ex 3<3 is false

Question 2

What is a Symmetric property?
What are some relations that use it?
What are some relations that don’t?

Answer 2

When a relation has a symmetric property, it means that if the relation is true between two things, it is true in either order. If A(relation)B, then B(relation).
Use it:
equality (11-3=8, 8=11-3)
congruence( tri A cong tri b, tri b cong tri A)
similarity
parallelism
perpendicularity
Don’t use it:
Strict inequalities don’t have a symmetric property. For example, [10 < 100], but 100 < 10 is false.

Question 3

What is a Transitive property?
What are some relations that use it?
What are some relations that don’t?

Answer 3

When a relation has a transitive property, then two things that relate to a common middle thing also relate to each other. If [A(relation)B] and [B(relation) C], then [A(relation)C].
use it:
Equality. ex m<A=m<b. m<A=m<c
then m<A=m<c
Congruence
similarity
Parallelism
Don’t use it:
Perpendicularity is not transitive.

Question 4

What is the difference between Equality & congruence

Answer 4

We use equality relations for anything we can express with numbers, including measurements, scale factors, and ratios.
We use congruence and similarity relations for geometric figures. We can’t perform arithmetic operations like addition and multiplication on geometric figures.